Let me ask two distinct questions: first, Did the universe begin to exist? and second, Does the universe have a cause? Since there are two conditions we are dealing with we can put the possible combinations of these conditions into four possible positions one could hold:
1. The universe began and it has a cause.
2. The universe didn't begin and it has a cause.
3. The universe began and it doesn't have a cause.
4. The universe didn't begin and it doesn't have a cause.
In theistic religions, 1 has been the most common option. But it should be noted that there were still some who held 2, that the universe, despite not having a beginning, still has a cause (such as Aristotle, Averroes, and the Latin Averroists). There is a good reason for this: simply showing the universe had no beginning is not sufficient to show that it has no cause; many forms of the cosmological argument argue from the premise of an infinitely-old universe.
Historically, the response of atheists was to accept 4, that the universe has neither a beginning nor a cause. Prior to the advent of Big Bang cosmology, position 3 was empty; at least I've never heard of anyone who accepted it, and the calls in the academic literature to find anyone who fits into it have gone unanswered. And yet it seems to be the position that atheists are driven to today. Of course, the fact that it has not been accepted historically does not mean that it is not a viable position to hold, but it surely gives us food for thought.
Ultimately, the claims that the universe began or that it did not amount to scientific predictions. The claim that it did have a beginning has been empirically verified by contemporary cosmology, and the claim that it did not has been empirically disconfirmed. And historically, the first category consists solely of theists, while the second category consists mostly of nontheists with a few theists. However, while theists argued for the universe's beginning, they did not think refuting this would refute theism -- in other words, while their prediction that the universe began could be falsified, their theism could not be (at least not by this factor). Atheists, however, gave no such indication: if you refuted the universe's eternality, then you would refute atheism, since it was accepted by all parties that if the universe began, it must have a cause. So the atheists' prediction was falsifiable, and by the same lights, so was atheism.
The problem, again, is that the atheists' prediction has been falsified. Thus, it would seem that atheism has been falsified. Yet atheists often claim to base their views on science and accuse theists of ignoring science. Surely this is backwards. Theists and atheists alike made a scientific prediction, the theists have had their prediction substantiated and the atheists have had their prediction refuted. In order to salvage their position, atheists have had to embrace a position that never occurred to anyone because it rejects the principle of causality. They have had to redefine their position so that it is no longer disproven by science. Again, this does not amount to a refutation of atheism, but if the tables were turned, do you think theists would be given the benefit of doubt?
(cross-posted at Quodlibeta)